Spectral properties of 438 GRBs detected by Fermi/GBM

A&A 530, A21 (2011) DOI:10.1051/0004-6361/201016270 c ! ESO 2011

Astronomy

&

Astrophysics

Spectral properties of 438 GRBs detected by

Fermi/GBM

!

L. Nava

_{, G. Ghirlanda}

_{, G. Ghisellini}

_{, and A. Celotti}

e-mail: lara.nava@sissa.it

2 _{Osservatorio Astronomico di Brera, via E. Bianchi 46, 23807 Merate, Italy}

Received 6 December 2010 / Accepted 26 January 2011

ABSTRACT

We present the results of the spectral analysis of the public data of 438 gamma ray bursts (GRBs) detected by the Fermi Gamma ray Burst Monitor (GBM) up to March 2010. For 432 bursts we could fit the time-integrated spectrum. In 318 cases we could reliably constrain the peak energy Eobs

peakof their νFνspectrum by analyzing their time-integrated spectrum between 8 keV and 35 MeV. Eighty

percent of these spectra are fitted by a power-law with an exponential cutoff, and the remaining with the Band function. Among these 318 GRBs, 274 belong to the long GRB class and 44 to the short. Long GRBs have a typical peak energy Eobs

peak∼160 keV and

low-energy spectral index α ∼ −0.92. Short GRBs have a harder peak low-energy (Eobs

peak∼ 490 keV) and a harder low-energy spectral index

(α ∼ −0.50) than long bursts. For each Fermi GRB we also analyzed the spectrum corresponding to the peak flux of the burst. On average, the peak spectrum has a harder low-energy spectral index than the corresponding time-integrated spectrum for the same burst, but similar Eobs

peak˙The spectral parameters derived in our analysis of Fermi/GBM bursts are globally consistent with those reported in

the GRB Cicular Network (GCN) archive after December 2008, while we found systematic differences in the low-energy power-law index for earlier bursts.

Key words.radiation mechanisms: non-thermal – Gamma rays: general

1. Introduction

Our current knowledge of the spectral properties of the prompt emission in GRBs mainly relies on the data collected in al-most ten years by the Burst And Transient Source Experiment (BATSE) onboard the Compton Gamma-Ray Observatory (CGRO). BATSE allowed characterization of the spectrum of the population of short and long GRBs over a wide energy range of 20 keV to 1–2 MeV. Analysis of such data revealed some important results about the spectral properties of these GRBs. The prompt spectra, integrated over the GRB duration (i.e. time-integrated spectra), can typically be described well by a curved function showing a peak – in a νFνrepresentation – at a

typi-cal energy Eobs

peakof a few hundred keV, but its distribution spans

nearly three orders of magnitude. Large dispersions also char-acterize the distributions of the low – and high – energy photon indices, whose characteristic values are α ∼ −1 and β ∼ −2.3, respectively (Band et al.1993; Ghirlanda et al.2002; Kaneko et al. 2006). Similar results are obtained by considering the time-resolved spectral analysis of flux/fluence limited samples of bright BATSE bursts (Preece et al.1998, 2000; Kaneko et al. 2006).

The BATSE data also suggest that there are two different classes of GRBs (long and short), based on both temporal and spectral features. Evidence of a spectral diversity between long and short bursts comes from their different hardness-ratios (HR) (Kouveliotou et al.1993). The higher HR of short bursts might be ascribed to a larger Eobs

peak. Nava et al. (2008) and Ghirlanda

et al. (2009 – G09 hereafter) showed that Eobs

peakcorrelates both

$ _{Tables 2–5 are available in electronic form at}

http://www.aanda.org

with the fluence and the peak flux. Although short and long bursts follow the very same Eobs

peak-peak flux relation, they obey

different (parallel) Eobs

peak-fluence relations. This obviously

im-plies that the distributions of the ratio Eobs

peak/fluence is different

for the two burst classes. Recently, Goldstein et al. (2010) have proposed this ratio as a discriminator between short and long GRBs. Owing to the relation between Eobs

peak and the

bolomet-ric fluence and peak flux, a direct comparison between the Eobs peak

distributions of the two different burst classes must take the dif-ferent fluence/peak flux selection criteria into account. G09 an-alyzed and compared samples of short and long BATSE bursts selected with similar peak flux limits. They found that the peak energy distributions of the two classes are similar, while the most significant difference is in the low-energy power-law indices, with short bursts typically having a harder α ∼ −0.4.

These global spectral properties of GRBs have also been confirmed by other satellites (BeppoSAX, Hete-II and Swift) (Guidorzi et al.2010; Sakamoto et al.2005; Butler et al.2007). However, the detectors onboard these satellites have different sensitivities than BATSE and cover a narrower and different energy range. For instance, the relatively narrow energy range (15–150 keV) of Swift/BAT does not allow the spectral peak Eobs

peakto be constrained for most of the detected bursts (Cabrera

et al.2007; Butler et al.2007).

Spectral studies of the prompt emission of GRBs require a wide energy range, possibly extending from a few tens of keV to the MeV energy range. This allows a measure of the curvature of the GRB spectrum and constraining its peak energy, as well as its low-and high-energy spectral slopes.

The Fermi satellite, launched in June 2008, represents a pow-erful opportunity to shed light on the origin of the GRB prompt

emission thanks to its two instruments: the Large Area Telescope (LAT) and the Gamma-ray Burst Monitor (GBM). LAT de-tected very high-energy emission (>100 MeV) from 19 GRBs in about two years. This emission component shares some com-mon features with what has already been found in a few bursts by EGRET (Energetic Gamma-Ray Experiment Telescope) on-board the CGRO satellite. In particular, high-energy ∼GeV flux is still observed when the softer energy emission (in the sub-MeV domain) ceases, and often its onset lags the sub-sub-MeV com-ponent (e.g. Ghisellini et al.2010; Omodei et al.2009).

The other instrument onboard Fermi is the GBM (Meegan et al. 2009), which is similar to BATSE and, despite its slightly worse sensitivity, allows study of the GRB spectrum over an un-precedentedly wide energy range, from 8 keV to 40 MeV. This is achieved by its twelve NaI detectors, giving a good spectral resolution between ∼8 keV and ∼1 MeV and two BGO detec-tors, which extend the energy range up to ∼40 MeV. Similar to BATSE, the NaI detectors guarantee full-sky coverage, but their smaller geometric area (16 times lower than that of the LADs of BATSE) implies a lower sensitivity. On the other hand, the presence of the BGO detectors allows the energy range to be extended for the first time for the study of the spectrum of the prompt emission to tens of MeV, thus accessing an energy range that is poorly explored with the CGRO instruments.

438 events, classified as GRBs1_{, triggered the GBM until the} end of March 2010. With this large sample of bursts we can per-form the first robust statistical study of the spectral properties of Fermi/GBM bursts. The main aims of this paper are (a) to present the results of the spectral analysis of 438 Fermi bursts, (b) to show the distribution of their spectral parameters, (c) to compare the spectral properties of Fermi short and long GRBs, and (d) to compare the spectra integrated over the burst dura-tion (time-integrated spectra, hereafter) with the spectra of the most intense phase of the burst, i.e. its peak flux (peak spectra, hereafter).

Preliminary results of the spectral analysis of Fermi GRBs performed by the GBM team have been distributed to the com-munity through the Galactic Coordinates Network (GCN) circu-lars. These amount to 228 GRBs (until March 2010), whereof 167 have a well constrained Eobs

peak. Ongoing spectral calibrations

of the GBM detectors mean that the results published in the GCN are “preliminary”, especially for the first bursts detected by the GBM. The GBM team continuously provides more updated de-tector response files, together with the public data of detected GRBs. A few months ago the software and the new response files were made public so that a systematic and reliable analysis of the spectra of Fermi/GBM bursts is now possible. We com-pare the results of our spectral analysis with those published in the GCN to search for possible systematic effects in the GCN results.

The paper is organized as follows. In Sects. 2 and 3 we de-scribe the sample of Fermi GRBs and the procedure adopted to extract and analyze their spectral data. In Sect. 4 we present the spectral results and build their distributions, while considering short and long GRBs separately. In Sect. 4 we also compare the time-integrated spectra and the peak spectra for the analyzed bursts. We summarize our results in Sect. 5.

1 _{http://heasarc.gsfc.nasa.gov/W3Browse/fermi/}

fermigbrst.html

2. The sample

The GBM detected 438 GRBs up to the end of March 2010. A list of the GRB trigger number and the position in the sky, com-puted by the GBM, is provided by the Fermi Science Support Center1_{. The data of each GRB have been archived and made}

public since July 2008. Since the only information given in the public archive is the burst position, it was not possible to apply any selection in flux, fluence, or duration on the GBM online public archive, since a spectral catalog is not available. For this reason we started the systematic analysis of GBM bursts in or-der to determine the spectral parameters, fluence, and peak flux of all bursts detected by Fermi/GBM up to March 2010.

Preliminary spectral results of Fermi GRBs have been dis-tributed by the GBM team through the GCN system. Starting on March 2010, the number of GCN of Fermi bursts substan-tially decreased, although the rate of detected bursts remained unchanged. We decided to limit our selection to March 2010, thus having a large sample of GCN results to compare with.

We collected all bursts with spectral information published in the GCN up to the end of March 2010 (228 objects). Among these, 148 long GRBs and 19 short have well-constrained spec-tral parameters, in particular the peak energy of their νFν. In

Sect. 4 we compare the GCN spectral parameters with those de-rived by us for the same bursts and search for possible systematic effects in the GCN results.

3. Spectral analysis

For the spectral analysis of Fermi/GBM bursts we used the re-cently released rmfit – v3.3pr7 software2_{. For each GRB to} be analyzed, the spectral analysis was done by combining to-gether more than one detector. Following the criterion adopted in Guiriec et al. (2010) and Ghirlanda et al. (2010), we selected the most illuminated NaI detectors having an angle between the source and the detector normal lower than 80 degrees. We se-lected the BGO #0 or #1 if the sese-lected NaI were all between #0-5 or #6-12, respectively. When the selected NaI were both be-tween #0-5 and #6-12, both BGO detectors were used. However, if one of the two BGO had a zenith angle to the source larger than 100 degrees we excluded it from the analysis.

The very wide available energy range (from 8 keV to ∼40 MeV) allows proper constraining of the peak energy of par-ticularly hard GRBs (with Eobs

peaklarger than 1 MeV, i.e. the upper

energy threshold of the NaI detectors) or the high-energy spec-tral power law, if present.

For the spectral analysis we used the CSPEC data (with time resolution of 1.024 s after the trigger time and 4.096 s before) for long GRBs and the TTE data (with time resolution of 0.064 s) for short GRBs. A first hint about the burst duration comes from the visual inspection of the lightcurves (at different temporal resolu-tions) stored in the quicklook directory provided with the data1_.

We used this method to decide which type of data (CSPEC or TTE) is more suitable for spectral analysis. Both data types con-tain spectra with 128 energy channels. Following the prescrip-tion of the rmfit tutorial3_{we considered the spectral data of the} NaI detectors in the range 8 keV–900 keV and for the BGO de-tectors in the range 250 keV–35 MeV.

For each GRB we extracted the background spectrum by se-lecting a time interval before and after the burst that was as large

2 _{http://fermi.gsfc.nasa.gov/ssc/data/analysis/} 3 _{http://fermi.gsfc.nasa.gov/ssc/data/analysis/user/}

as possible, but distant enough from the burst signal to avoid burst contamination. The spectra in these two time intervals were modeled in time with a polynomial of order between 0 and 4 to account for the possible time evolution of the background. Then, the spectral analysis software extrapolates the background to the time interval occupied by the burst. We used the most updated response files with extension rsp2, which allows rmfit to use a new response for each 5 deg of spacecraft slew, as explained in the rmfit tutorial.

Each spectrum was analyzed by adopting the Castor statis-tics (C-stat). Since we combined NaI and BGO detectors in the spectral analysis, we fitted the spectra by allowing for a calibra-tion constant among the different detectors. The spectral results (C-stat and spectral parameters) obtained with the calibration constants free and fixed to 1 were compared. If no significant difference was found between the C-stat and the spectral param-eters obtained in these two cases, the calibration constants were fixed to 1 (as also suggested in the rmfit manual). In nearly 30% of the cases, the C-stat significantly decreased by using free cal-ibration constants. This is not directly related to the burst bright-ness (also for faint bursts the calibration constants can be re-quired) even if, of course, the largest differences in C-stat values are found for bright bursts, since possible calibration offsets be-tween instruments strongly affect the fit (in terms of C-stat) when data points have small errors.

Systematic residuals around the k-edge of the NaI detec-tors are often visible, owing to calibration issues (Guiriec et al. 2010). For four bursts (for which this effect is particularly pro-nounced), we performed the spectral analysis both including and excluding a few channels between 30 keV and 40 keV (e.g. see Guiriec et al.2010). While the spectral parameters and their er-rors are not sensitive to this choice, the value of the C-stat is quite different. For these four bursts we report the results of both the analyses (Table 2).

3.1. Spectral models

The spectral analysis performed by different authors (Preece et al.2000; Sakamoto et al.2005; Kaneko et al. 2006; Butler et al. 2007; Nava et al. 2008; Guidorzi et al. 2010) on data taken from different instruments revealed that GRB spectra are fitted by different models, the simplest ones being i) a single power-law model (PL), ii) a Band function (Band et al.1993), which consists of two smoothly connected power-laws and iii) a Comptonized model (CPL hereafter), i.e. a power-law with a high-energy exponential cutoff.

The time-resolved spectra of BATSE GRBs have been also fitted by combining thermal (black-body) and nonthermal (power-law) models (e. g. Ryde et al.2005; Ryde et al.2009). Although these fits are intriguing for their possible physical implications (Pe’er et al. 2010), they are statistically equiva-lent to fits with the phenomenological models described above (Ghirlanda et al. 2007). Recently, Guiriec et al. (2010) have found evidence of a thermal black body component (summed to the standard Band function) in the spectrum of the Fermi GRB 100724B.

A simple PL function clearly indicates that no break/peak energy is detected within the energy range of the instrument. Furthermore, it is also statistically the best choice when the signal-to-noise ratio of the analyzed spectra is very low because this model has the lowest number of free parameters. This was shown, for instance, by the analysis of the Swift/BAT spectral data (e.g. Cabrera et al.2007).

The Band model (Band et al.1993) has four free parameters to describe the low and high power law behaviors, the spectral break and the flux normalization. Typically, the low-energy pho-ton index α > −2 [N(E) ∝ Eα_{] and the high-energy photon index}

β <_{−2 [N(E) ∝ E}β_{], so that a peak in νF}

νcan be defined. When

there is no evidence of a high-energy photon tail or Eobs peakis near

the high-energy boundary of the instrument sensitivity (and β is poorly constrained), a CPL model is preferred due to the lower number of parameters. Also in this case a peak energy can be defined when α > −2. In the Band model the spectral curvature is fixed by α, β, and Eobs

peak.

We fitted all these nested models to each GRB spectrum. The addition of one free parameter requires an improvement in C-stat of 9 for a 3σ confidence in this improvement. We chose this criterion to select the best-fit model. In addition, we also required that all the spectral parameters are well determined (i.e. no upper or lower limits).

3.2. Time integrated and peak flux spectra

As anticipated we analyzed, for each burst, (1) the spectrum inte-grated over its whole duration and (2) the spectrum correspond-ing to the peak of the burst. For the peak spectrum, this could be selected from the raw-count light curve as the temporal bin with the highest count rate. However, it may happen that bins with a similar count rate have very different spectra, and their flux can be considerably different. Therefore, a more physical approach for identifying the peak of the burst is to build its flux light curve (i.e. calculating the flux in physical units). In practice, we per-formed a time-resolved spectral analysis of each burst and built its flux light curve, where the flux is integrated over the 8 keV– 35 MeV energy range, i.e. the same spectral range where the spectral analysis is performed). Then we identified the time bin corresponding to the largest flux and analyzed this spectrum to extract the peak spectrum parameters. As timescale for the time-resolved spectral analysis, we chose 1.024 and 0.064 seconds for the long and short GRBs, respectively. We adopt this procedure for all GRBs, i.e. even those having a time-integrated spectrum better described by a simple power-law.

4. Results

The spectral parameters obtained from analysis of the time-integrated spectra of the 438 Fermi/GBM bursts are reported in Tables2and3. In particular, in Table2we list all the 323 bursts whose spectrum could be fitted with either the Band or CPL model (Col. 3). In five cases, the high-energy power-law index β is >−2, and this reduces the number of bursts with well-defined peak energy Eobs

peakto 318. In Table3we report all the 109 cases

where a single power-law is the best fit to the data and the 6 cases where spectral analysis was impossible for lack of data.

In both tables we give the time interval over which the time-integrated spectrum was accumulated and the best-fit model (Cols. 2, 3), the normalization constant (Col. 4) in units of photons cm−2 _s−1 _{(computed at 100 keV for all models), and}

the spectral index α (Col. 5) of the low-energy power-law. The peak energy of the νFνspectrum and (for the spectra fitted with

the Band model) the high-energy spectral index β are listed in Cols. 6 and 7 of Table2, respectively. We also report in both tables the value of the C-stat resulting from the fit and the as-sociated degrees of freedom (d.o.f.). The last column in Table2 gives the fluence obtained by integrating the best-fit model over the 8 keV–35 MeV energy range. For the spectra fitted with

the PL model, we give the fluence (last column in Table 3) computed over a narrower energy range, 8 keV–1 MeV, be-cause we could not identify where the peak energy is. For four bursts (GRB 081009140, GRB 090618353, GRB 090626189, and GRB 090926181), we performed the spectral analysis both including and excluding a few channels around the k-edge. In these cases, we report both the results in the tables. In 19 cases we found that the fit with a Band model returns well constrained parameters, but it is not statistically preferred to the Comp model (the C-stat improvement is lower than 9). In these cases we list the parameters of both models in the tables.

In Table4we report the results of the peak spectra analysis. In particular, we list the initial (t1) and final (t2) times of the

se-lected temporal bin, the best-fit model, its spectral parameters, C-stat, and degrees of freedom. The last column lists the peak flux estimated in the 8 keV–35 MeV energy range. Finally, in Table5, we list the spectral properties and the fluence collected from the GCN Circulars. For each burst we also report the red-shift (when available) and the GCN number.

4.1. Time-integrated spectra

Out of the 432 bursts for which it was possible to perform the spectral analysis, 359 are long and 73 short. In the case of long (short) bursts, 274 (44) events have a well-defined peak energy, while 4 (1) are best fitted with a Band model with β > −2. Most of the spectra are adequately fitted by the CPL model. This is true for both the long and short subgroups. Among the 109 spec-tra fitted with a simple power-law model, there are 81 and 28 long and short events.

In our analysis we integrated the spectrum over a time in-terval (∆T ) where the signal of the burst (for all NaI detectors combined) is stronger than the average background. Therefore, we adopt this integration time to separate short and long GRBs (i.e. ∆t < 2 s and ∆t > 2 s, respectively). The distribution of ∆t is bimodal and short and long GBM bursts are separated into two log normal distributions with central value (standard deviation) %Log(∆t)& = 1.42 (σ = 0.39) and %Log(∆t)& = −0.33 (σ = 0.38) for long and short GRBs, respectively.

Fluence distribution – In Fig.1we show the LogN − LogF distributions of the Fermi GRBs analyzed. To show the fluence distribution of all the 432 GRBs that we could successfully fit, we computed the fluence in the 8 keV–1 MeV for the 323 GRBs fitted with either the Band or CPL model and for the 109 GRBs fitted with a power-law. We show separately the LogN−LogF for long (359 events) and short (73 events) GRBs. At large fluences the distribution of long and short has a very similar slope to the euclidean one (–3/2), which is shown for comparison. In Fig.2 we show the LogN − LogF distribution by dividing our sample according to the best-fit model.

Epeakdistribution – In Fig.3we show the peak energy

dis-tribution of the 318 GRBs (both long and short) and the fit with a Gaussian. Also, in Fig. 3 short and long events are shown separately and the Kolmogorov-Smirnov test gives a probabil-ity PKS= 3.4× 10−15that the two distributions of Eobs_peakfor long

and short GRBs are drawn from the same parent distribution. Spectral index distributions – In Fig.4we show the distribu-tion of the low-energy spectral index α for all the 318 GRBs and for short and long GRBs separately (having a PKS = 7.3×10−12).

Finally, in Fig.5 we show the distribution of the high-energy spectral index β for the 60 time-integrated spectra that are fitted with the Band model (see Table2).

Fig. 1.LogN − LogF of the 432 GRBs analyzed in this work (Tables2 and3). Short GRBs (73 events) and long GRBs (359 events) are shown with (red) triangles and (blue) circles, respectively. The black histogram refers to the entire sample. The dashed and dot-dashed lines are two power-laws with slope –3/2. The fluence F in erg/cm2 _{is obtained by}

integrating the best-fit model in the 8 keV–1 MeV energy range.

Fig. 2.LogN − LogF distributions of all the GRBs fitted with the CPL or Band model and well-constrained Eobs

peak (pink circles) and of the

109 GRBs fitted with a single PL model (green triangles). For reference a power law with slope –3/2 is shown (dashed and dot-dashed line). The fluence F in erg/cm2_{is obtained by integrating the best-fit model in the}

8 keV–1 MeV energy range.

All the parameters distributions shown in Figs.3and4 are fitted by Gaussian functions whose parameters are reported in Table1.

4.2. Peak spectra

For each burst we also extracted and analyzed the spectrum cor-responding to its peak flux. To this aim, we performed a time-resolved spectral analysis of each burst. In the flux light curve, we then selected the time bin with the largest flux. The timescale is given by the resolution of the data, i.e. typically 1.024 s and 0.064 s for long and short GRBs, respectively. We also verified that in most cases the peak of the count rate coincides with the peak of the flux.

Fig. 3.Distribution of the peak energy for the GRBs listed in Table2 fitted with either the Band or CPL model and with determined Eobs

peak

(318 GRBs). The solid line shows the fit with a Gaussian. Also shown (hatched blue and red histograms) are the distributions for 274 long and 44 short GRBs, respectively, and their Gaussian fits (dot-dashed and dashed lines for long and short events, respectively).

Fig. 4.Distribution of the low-energy photon index for the 318 GRBs listed in Table2fitted with either the Band or CPL model and with determined Eobs

peak. The solid (black) line shows the fit with a Gaussian.

Also shown (hatched blue and red histograms) are the distributions for 274 long and 44 short GRBs, respectively, and their Gaussian fits (dot-dashed and (dot-dashed line for long and short events, respectively).

Out of the 432 analyzed GRBs, the peak spectrum could be extracted and fitted with a Band or CPL model in 235 cases. As before, the best-fit model is defined by requiring an improvement in the C-stat value of 9 (between a given model and a more com-plex one with one parameter more) and well-constrained spectral parameters. In 27 cases (26 long and 1 short) the best-fit model of the peak spectrum is different from that of the time-integrated spectrum. The spectral parameters of the peak spectra fitted with these two models are reported in Table4.

In Fig.6we compare the peak energy Eobs

peakand the low

spec-tral index α at the peak flux with the values of the time-integrated spectrum for bursts having all this information (227 events.). Empty (filled) symbols refer to GRBs for which the time-integrated and the peak spectra are described by the same (a dif-ferent) best-fit model. On average, the time-integrated and peak

Fig. 5.Distribution of the high-energy photon index for 60 GRBs whose time-integrated spectrum is best fit with the Band model.

Table 1. Parameters of the Gaussian fits of the distributions of the

spec-tral parameters of Fermi/GBM bursts analyzed in this work. Parameter Type # of GRBs Central value σ Log(Eobs peak) All 318 2.27 0.40 Short 44 2.69 0.19 Long 274 2.21 0.36 α All 318 –0.86 0.39 Short 44 –0.50 0.40 Long 274 –0.92 0.35

spectrum values of Eobs

peakare very similar, while the low-energy

spectral index, at the peak, is harder. 4.3. Comparison with GCN results

Since August 2008, the Fermi GBM team is providing prelim-inary results of the spectral analysis of a large number of the detected GRBs through the GCN Circulars. For each burst, the GCN circular reports the burst’s duration, spectral parameters, fluence, and photon peak flux (all with their associated errors). GCN circulars are promptly released when a burst occurs and are not updated after their first release. On the other hand, the GBM team is continuously providing, through the online archive, new versions of the detector response files, improved with respect to the first version used to perform their preliminary analysis. Our analysis benefits from the most updated response files. A mean-ingful comparison between our results and those preliminarily reported by the GBM team must account for this difference.

It is likely that the calibration of the different detectors has changed and been improved from the earliest to the latest circu-lar, along with the software and tools used by the Fermi team. If this is the case, spectral parameters of the first bursts detected by Fermi and reported in the GCN could be affected by system-atic biases, hopefully not present in our analysis. To verify this possibility, we plotted the spectral parameters (α and Eobs

peak) as

a function of the date (in MJD) of the GRB detection, to point out any possible systematic trend of their values and/or associ-ated uncertainties. The spectral parameters (from our sample and from the GCN sample) are plotted in the upper panels of Fig.7. In the GCN sample, long bursts (Fig.7) detected at the be-ginning of the mission have a slightly harder α with respect to

Fig. 6.Comparison of time-integrated and peak-flux spectral parameters for the 227 GRBs whose peak spectrum could be fitted with the Band or CPL model (reported in Table4and present also in Table2). Top

panel: peak energy. Bottom panel: low-energy spectral index (α). Empty (filled) symbols are GRBs for which the time-integrated and the peak flux spectra have same (different) best fit model. Squares refer to short events and circles to long events.

the following bursts and also to the same bursts analyzed by us. This trend is not present in the short burst sample. In this case, however, the sample is small, and short bursts are only present in the GCN sample starting from December 2008.

A possible bias on the α values can be better quantified by probing how the α distribution for long bursts evolves in time. After having sorted GRBs according to their increasing date of detection, we consider the distribution of the spectral parameter up to a certain date and we fit it with a Gaussian function by deriving its central value and the standard deviation. This corre-sponds to showing how the cumulative distributions change by increasing the time span. Since a systematic difference in α be-tween our analysis and what is reported in the GCNs might also be ascribed to a systematic difference in the choice of the best-fit model, we use only those bursts for which the best-fit model is the same in both analyses.

Our test starts on November 2008, when we start to have enough bursts for a reliable Gaussian fit. The middle left panel in Fig.7 shows our results. The y-axis shows the central value of the Gaussian fit and the error bar correspond to its 1σ width. In the GCN sample a trend is clearly visible. Although at the 1σ level we see that all the central values are consistent, the mean

of α (∼−0.5 at the beginning) systematically evolves from harder to softer values, and then it levels off at about –0.85. This result rules out the possibility that the bias is due to a different choice in the best-fit model and suggests that another nonphysical ef-fect could be biasing the low-energy power-law indices towards harder values in the first months of the GCN data analysis. This trend is not present in our sample (Fig.7, middle left panel), for which the α distribution does not evolve in time.

The whole α distributions for the two different samples are somewhat different, with the GCN sample having slightly harder spectral indices (%α& = −0.86 compared to %α& = −0.92 derived from our analysis), as shown by the last point in the middle-left panel of Fig.7. We are interested in understanding whether this difference can be totally ascribed to the bias affecting the first bursts and, in this case, in determining the date from which GCN preliminary results are consistent with those obtained by our analysis with the most updated response files. The bottom panels of Fig.7show the average values of α and Eobs

peakfor two

different periods of time: up to the end of December 2008 and from January 2009 to March 2010.

Figure 8 shows the difference ∆α between the low-energy spectral indices as reported in the GCN sample and as derived by us for bursts common to both samples. The upper panel shows bursts fitted with the same best-fit model in both analyses (i.e. the same subsample as used in Fig.7). The bottom panel, in-stead, shows all bursts common to both samples. Approximately up to the end of December 2008, this difference is not randomly distributed around ∆α = 0, but is systematically larger. This jus-tifies our choice of considering these two time intervals for the bottom panels of Fig.7, showing that bursts in the GCN sample up to the end of December 2008 have a mean α = −0.5, while the αdistribution of the remaining bursts is peaked around α = −0.9, perfectly consistent with our results. The same separation has been applied to our sample, which does not show any difference in α when comparing bursts before and after December 2008 (bottom left panel in Fig.7).

The Eobs

peakvalues (right panels in Fig. 7) are untouched by

this effect. The results from the two different samples are highly consistent. A weak trend is visible, but the central value of the Eobs

peakdistribution spans 130 keV to 150 keV, a very narrow range

if compared to the width of the distribution and to the typical errors on this parameter.

5. Summary and conclusions

We analyzed the spectra of all GRBs detected by the Fermi/GBM between 14 July 2008 and 30 March 2010. There are 438 GRBs, and for 432 of them we have all the data needed to perform the spectral analysis. The time-integrated spectrum is best fit-ted with a power-law model (110 spectra-reporfit-ted in Table3) or a curved model (323 spectra – reported in Table2), which is either the Band model (65 spectra) or a cutoff-power-law (CPL) model (258 spectra).

Among the 432 GRBs for which we could analyze the spec-trum, we identify 73 short and 359 long bursts. Their LogN − LogF is similar (Fig.1) and its high-fluence tail is consistent with a power law with slope –3/2.

The 73% of the bursts detected by the GBM up to March 2010 could be fitted with a curved model (Band or CPL, with a prevalence of the latter model) and in the majority (318 out of 323) of these cases we could constrain the spectral parameters, in particular, the peak energy Eobs

peakof the νFνspectrum. This is

Fig. 7.Comparison of GCN preliminary results and our analysis. Upper panel: crosses and squares show (for long and short events respectively) the time trend of the spectral properties (α on the left and Eobs

peakon the right) for GBM bursts whose preliminary spectral analysis has been reported

in the GCN circulars. Circles and stars show the same for the sample of long and short bursts analyzed by us. We show only those bursts for which the same spectral models were used in our analysis and in the analysis reported in the GCN circulars. Time on the x-axis is in MJD units. Middle

panels: central values and 1σ width for the α (left) and Eobs

peak(right) distributions (long bursts only) for the GCN sample (crosses) and our sample

(circles) as a function of time. Bottom panels show the average α and Eobs

peakfor two different periods of time, up to and after December 2008. extending from 8 keV to ∼35 MeV. This is the sample we

con-sidered for characterizing the spectral parameters of the time-integrated spectra of Fermi GRBs. Within this sample there are 44 short and 274 long GRBs. The comparison of their spectral properties shows that short GRBs have higher Eobs

peakthan do long

events (Fig.3) and a slightly harder low-energy spectral index α (Fig.4).

The finding that short Fermi GRBs have harder peak energy than long events seems opposite to what has been found from the comparison of short and long GRBs detected by BATSE (Ghirlanda et al. 2009).

However, the Fermi short GRBs also have larger peak fluxes than long events. A more detailed comparison between long and short GRBs detected by Fermi/GBM and BATSE is presented in Nava et al. (2010).

A second major part of the present work was to character-ize the spectra of the peak of each GRB. Through time-resolved spectroscopy, we isolated and analyzed the spectrum corre-sponding to the peak of the flux light curve of each burst. The results are reported in Table4. By comparing the peak spectrum and the time-integrated spectrum of individual GRBs, we find that the peak spectra have similar Eobs

peak of the time-integrated

spectra but harder low-energy spectral index α (Fig.6).

Finally we compared the results of our spectral analysis with those reported in the GCN circulars. We found that the still not fully completed calibrations of the GBM detectors means that the GCN results of bursts comprised between July and December 2008 are affected by a systematic overestimate of the hardness of the GRB spectrum at low energies (i.e. the spectral parameter α).

Fig. 8.Difference between α values reported in the GCN Circulars and αvalues derived from our analysis. Top panel: bursts for which the spec-trum is described by the same model both in our analysis and in the GCN analysis. Bottom panel: bursts common to both samples regard-less of the spectral model chosen to describe the spectrum.

This systematic bias does not affect Eobs

peakand is not present in

our results, which were obtained with the most recent releases of the GBM response files.

Acknowledgements. This research has made use of the public Fermi/GBM data and software obtained through the High Energy Astrophysics Science Archive Research Center Online Service, provided by the NASA/Goddard Space Flight Center. We acknowledge the GBM team for the public distribution of the spec-tral properties of Fermi/GBM bursts through the GCN network. We thank the referee for his/her useful comments. This work has been partly supported by ASI grant I/088/06/0. L.N. thanks the Osservatorio Astronomico di Brera for the kind hospitality for the completion of this work.

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Table 2. Spectral parameters of the time-averaged spectra of 323 Fermi/GBM GRBs fitted with a curved function.

GRB ∆t Model aA/10−3 α Epeak β C-stat d.o.f. Fluence/10−7

s ph/cm2_{/s keV erg/cm}2 080714745 28.672 CPL 8.79± 1.41 –1.14± 0.07 167.7± 16.7 ... 765.53 595 73.75± 3.73 080715950 14.336 CPL 7.57± 0.48 –1.27± 0.04 315.5± 38.4 ... 784.04 712 59.74± 3.16 080717543 26.624 Band 10.92± 3.55 –0.66± 0.18 119.1± 19.8 –2.11± 0.17 740.76 462 85.89± 19.96 080719529 44.032 CPL 4.67± 2.50 –0.56± 0.30 92.56± 15.0 ... 450.01 348 14.87± 1.81 080723557 73.728 Band 34.02± 0.72 –0.85± 0.01 194.0± 3.7 –2.43± 0.05 1281.70 468 1011.00± 32.41 080723913 0.32 CPL 38.28± 14.60 –0.24± 0.30 168.7± 26.3 ... 375.81 355 1.66± 0.20 080723985 60.417 CPL 10.18± 0.24 –0.98± 0.02 427.4± 18.7 ... 597.02 472 412.89± 9.67 080724401 120.834 Band 9.50± 0.86 –0.97± 0.05 97.96± 4.86 –2.33± 0.09 889.96 591 270.22± 20.53 080725435 37.888 CPL 5.64± 0.29 –1.08± 0.04 322.6± 28.3 ... 551.75 474 110.54± 4.93 080725541 0.512 CPL 10.87± 1.25 –0.73± 0.09 1439± 376 ... 599.68 594 17.58± 3.38 080727964 81.921 CPL 3.51± 0.18 –1.33± 0.03 314.4± 36.5 ... 1166.4 708 164.18± 8.19 080730520 24.576 CPL 9.77± 0.93 –0.84± 0.06 151.9± 8.63 ... 714.57 582 47.07± 1.67 080730786 10.24 Band 48.67± 3.72 –0.53± 0.04 113.3± 3.11 –3.05± 0.21 646.78 589 55.54± 2.25 080730786 10.24 CPL 43.41± 2.61 –0.59± 0.04 119.4± 2.53 ... 654.99 590 48.98±6.86 080802386 0.384 CPL 24.24± 2.75 –0.73± 0.12 601.4± 124.0 ... 401.88 355 9.66± 1.34 080804456 33.792 CPL 3.61± 0.58 –0.99± 0.10 144.0± 15.7 ... 642.52 592 26.38± 1.73 080804972 31.744 CPL 9.14± 0.52 –0.72± 0.04 252.7± 13.6 ... 757.72 589 98.78± 3.49 080805584 68.609 CPL 4.33± 1.07 –1.02± 0.13 84.23± 8.39 ... 567.19 349 37.89± 2.74 080806584 7.168 CPL 32.32± 23.30 –0.23± 0.37 56.85± 5.15 ... 350.25 353 4.41± 0.36 080806896 92.162 Band 22.81± 4.98 –0.75± 0.10 49.77± 2.56 –2.27± 0.05 1579.80 703 177.11± 34.11 080807993 27.648 CPL 4.05± 0.25 –1.04± 0.04 883.3± 191.0 ... 655.21 586 153.10± 20.19 080808565 25.6 Band 16.70± 2.53 –0.99± 0.07 67.49± 3.44 –2.83± 0.22 554.83 480 49.20± 2.75 080808565 25.6 CPL 14.42± 1.51 –1.06± 0.05 72.12± 2.45 ... 558.3 481 42.23±0.89 080808772 178.18 CPL 5.11± 1.21 –0.72± 0.12 62.69± 3.0 ... 622.82 476 48.78± 2.32 080809808 34.816 CPL 7.52± 1.73 –1.29± 0.12 62.96± 5.18 ... 343.36 240 40.18± 1.95 080810549 81.921 CPL 2.57± 0.09 –1.38± 0.02 944.8± 203.0 ... 928.83 599 252.41± 23.76 080812889 30.72 CPL 9.96± 3.06 0.13± 0.24 146.3± 13.10 ... 457.14 356 23.30± 1.74 080816503 58.369 Band 13.71± 0.88 –0.92± 0.04 124.3± 5.2 –2.49± 0.13 972.74 595 197.74± 16.32 080816989 3.6 CPL 5.60± 0.23 –0.67± 0.06 1637± 226 ... 741.75 599 81.37± 9.02 080817161 91.137 Band 11.43± 0.25 –0.94± 0.02 358.0± 13.5 –2.33± 0.07 825.12 474 906.81± 50.13 080818579 33.793 CPL 2.87± 0.45 –1.33± 0.09 137.2± 21.9 ... 530.05 479 29.60± 4.51 080818945 15.36 CPL 5.73± 1.00 –1.45± 0.09 69.36± 6.26 ... 506.83 475 19.45± 1.01 080821332 10.24 CPL 16.16± 1.79 –0.97± 0.06 119.10± 7.31 ... 388.62 356 28.40± 0.99 080823363 41.984 CPL 3.36± 0.31 –1.31± 0.05 205.2± 26.0 ... 778.63 597 57.27± 3.28 080824909 28.672 CPL 5.30± 0.63 –1.12± 0.07 160.9± 17.4 ... 555.98 476 42.21± 6.30 080825593 41.984 Band 34.48± 1.13 –0.69± 0.02 189.2± 4.91 –2.34± 0.06 771.61 711 567.08± 28.12 080829790 14.336 Band 71.82± 41.60 –0.10± 0.27 54.69± 5.0 –2.36± 0.11 327.71 356 28.77± 3.58 080831921 81.921 CPL 17.98± 2.70 –0.39± 0.09 89.78± 2.96 ... 677.80 475 79.81± 2.29 080904886 25.6 CPL 29.13± 2.98 –1.14± 0.05 39.24± 0.75 ... 668.75 587 52.15± 0.95 080905499 0.704 Band 26.28± 9.09 0.66± 0.40 284.6± 47.9 –2.15± 0.17 678.34 594 14.70± 3.24 080905499 0.704 CPL 13.00± 1.65 -0.13± 0.16 515.6± 69.0 ... 683.02 595 9.28± 0.92 080905570 38.912 CPL 6.18± 0.98 –1.21± 0.08 84.29± 6.49 ... 421.47 357 40.99± 1.69 080906212 7.168 Band 53.09± 4.21 –0.51± 0.05 153.4± 7.26 –2.20± 0.08 649.34 597 120.21± 11.47 080913735 29.696 CPL 8.02± 1.70 –0.70± 0.12 106.6± 8.57 ... 376.09 352 25.55± 1.37 080916009 88.581 Band 13.49± 0.23 –1.05± 0.01 515.8± 22.4 –2.16± 0.06 972.11 597 1707.70± 88.50 080916406 60.417 CPL 6.38± 0.59 –0.99± 0.05 123.4± 6.51 ... 583.16 482 70.24± 2.12 080920268 43.008 CPL 3.19± 0.80 –0.50± 0.17 162.8± 19.9 ... 587.82 478 21.79± 1.76 080924766 41.984 CPL 3.53± 0.47 –1.34± 0.07 109.5± 11.1 ... 610.30 600 38.49± 1.81 080925775 35.84 Band 18.65± 0.89 –1.03± 0.03 156.8± 7.07 –2.29± 0.08 807.43 716 278.00± 20.43 080927480 43.008 Band 88.08± 105.00 0.39± 0.53 52.3± 8.36 –1.95± 0.08 522.37 358 101.33± 21.10 081008832 79.873 CPL 2.89± 0.22 –1.15± 0.04 252.7± 26.5 ... 878.39 602 98.74± 5.51 081009140 40.96 CPL 51.61± 1.64 –1.66± 0.02 27.22± 0.59 ... 463.43 348 419.6± 2.30 081009140 40.96 CPL 54.66± 1.66 –1.64± 0.02 28.11± 0.53 ... 607.75 357 419.4± 2.34 081009690 35.84 Band 35.28± 11.50 –0.46± 0.15 69.45± 7.19 –1.88± 0.04 607.21 477 259.21± 7.39 081012045 0.96 CPL 11.35± 1.08 –0.60± 0.10 771.7± 139.0 ... 494.99 477 16.92± 2.21 081012549 23.552 CPL 4.82± 0.77 –0.23± 0.15 273.5± 30.6 ... 618.62 589 36.15± 3.06 081021398 44.033 CPL 8.44± 1.41 –0.90± 0.10 116.0± 9.44 ... 503.39 358 56.53± 2.82 081024851 81.921 Band 15.21± 6.64 –0.83± 0.19 45.38± 4.55 –2.19± 0.06 1037.10 598 123.99± 10.64 081024851 81.921 CPL 4.10± 0.47 –1.33± 0.06 73.8± 3.69 ... 1042.0 599 63.64±1.8 081025349 25.6 CPL 7.49± 0.63 –0.53± 0.07 251.8± 16.3 ... 859.68 723 59.46± 2.77 081028538 19.456 CPL 18.75± 4.25 –0.70± 0.12 65.02± 3.1 ... 560.24 473 19.81± 0.70 081101491 0.704 CPL 12.34± 4.24 –0.34± 0.32 249.0± 54.4 ... 510.31 479 2.45± 0.59 081101532 9.725 CPL 23.46± 1.06 –0.70± 0.03 468.7± 20.3 ... 604.63 598 172.79± 4.96 081102365 2.5 CPL 6.84± 0.60 –0.73± 0.10 656.3± 131.0 ... 592.09 599 19.82± 2.52 081102739 46.081 CPL 9.61± 1.74 –0.55± 0.11 99.37± 5.58 ... 623.76 481 35.24± 1.45

Table 2. continued.

GRB ∆t Model aA/10−3 α Epeak β C-stat d.o.f. Fluence/10−7

s ph/cm2_{/s keV erg/cm}2 081107321 3.0 CPL 100.80± 13.60 –0.51± 0.07 70.1± 1.7 ... 867.86 717 13.34± 0.26 081109293 36.864 CPL 3.86± 0.36 –1.42± 0.05 200.5± 31.9 ... 906.22 710 63.21± 4.43 081110601 20.48 CPL 7.13± 0.37 –1.12± 0.04 361.6± 35.7 ... 523.29 478 85.20± 4.30 081115891 0.32 CPL 9.63± 2.57 0.26± 0.45 467.0± 119.0 ... 781.88 715 2.90± 0.74 081118876 19.965 Band 68.24± 15.40 –0.46± 0.10 56.79± 2.77 –2.29± 0.05 698.79 601 81.59± 5.19 081121858 26.624 Band 28.77± 3.39 –0.46± 0.08 172.8± 11.5 –2.19± 0.07 411.33 353 284.07± 24.50 081122520 21.504 CPL 12.92± 0.78 –0.83± 0.04 206.5± 10.6 ... 761.16 717 78.37± 2.36 081124060 24.576 Band 30.68± 7.82 –1.70± 0.09 10.33± 1.58 –2.71± 0.03 1007.00 718 104.26± 2.95 081125496 10.365 Band 104.00± 6.47 –0.46± 0.04 165.8± 4.69 –2.85± 0.14 667.48 596 213.65± 9.74 081126899 38.912 CPL 5.63± 0.31 –0.97± 0.04 343.6± 29.9 ... 595.53 478 116.89± 5.45 081129161 26.749 Band 16.32± 1.33 –0.85± 0.05 202.7± 17.1 –2.08± 0.10 429.12 354 284.24± 34.77 081130629 15.36 CPL 5.15± 0.78 –1.06± 0.09 160.2± 18.8 ... 532.57 477 20.54± 1.31 081204004 4.096 CPL 9.74± 2.01 –0.71± 0.14 193.2± 27.4 ... 539.29 479 9.48± 0.90 081204517 0.384 CPL 25.79± 6.21 –0.71± 0.17 220.4± 44.0 ... 495.78 479 2.79± 0.39 081206275 22.528 CPL 7.48± 0.98 –0.47± 0.10 227.1± 17.8 ... 1222.50 477 43.45± 2.48 081207680 103.43 Band 9.37± 0.27 –0.58± 0.02 375.1± 13.2 –2.22± 0.07 1040.40 596 1046.40± 69.28 081209981 0.32 Band 33.19± 2.16 –0.67± 0.07 1057± 192 –2.25± 0.20 478.37 470 39.29± 5.43 081209981 0.32 CPL 35.80± 2.28 –0.714± 0.05 1256± 162 ... 482.56 471 30.91± 2.85 081215784 9.468 Band 94.00± 1.29 –0.72± 0.01 417.5± 8.6 –2.32± 0.03 667.83 475 957.61± 22.71 081215880 17.408 Band 15.86± 5.28 –0.40± 0.21 122.2± 14.7 –2.51± 0.28 500.84 482 39.35± 7.83 081215880 17.408 CPL 11.12±2.00 –0.61± 0.13 145.0± 11.0 ... 502.95 483 28.65±1.50 081216531 0.768 CPL 34.90± 2.22 –0.75± 0.04 1161.0± 121.0 ... 672.08 599 63.26± 4.69 081217983 58.368 CPL 5.66± 0.35 –1.05± 0.04 189.7± 11.2 ... 876.48 599 100.14± 3.09 081221681 39.422 Band 71.87± 1.93 –0.82± 0.01 85.86± 0.74 –3.73± 0.20 999.80 600 281.93± 3.35 081221681 39.422 CPL 69.47± 1.65 -0.83±0.01 87.15±0.62 ... 1006.1 601 271.8±1.3 081222204 21.504 Band 21.08± 1.15 –0.90± 0.03 167.2± 8.28 –2.33± 0.10 744.67 604 175.58± 16.33 081223419 0.832 CPL 42.27± 4.68 –0.69± 0.08 193.2± 14.1 ... 625.15 601 8.27± 0.39 081224887 19.614 CPL 31.30± 0.44 –0.82± 0.01 428.8± 9.48 ... 557.12 481 412.31± 5.88 081226044 0.448 CPL 15.05± 2.53 –0.75± 0.18 493.8± 132.0 ... 484.56 476 5.42± 0.91 081226156 80.897 CPL 2.09± 0.28 –1.47± 0.07 86.23± 8.05 ... 607.11 482 45.46± 2.03 081226509 0.448 CPL 17.53± 2.58 –0.46± 0.16 422.1± 73.4 ... 651.05 602 5.26± 0.67 081229187 0.512 CPL 13.04± 2.06 –0.31± 0.20 509.3± 97.8 ... 700.39 598 6.24± 0.92 081231140 41.985 CPL 9.82± 0.28 –1.21± 0.02 255.7± 11.0 ... 777.75 600 185.35± 3.72 090101758 46.08 CPL 12.6± 0.74 –1.18± 0.03 115.2± 4.67 ... 669.54 477 125.8± 2.63 090102122 38.912 CPL 12.35± 0.30 –0.97± 0.01 461.1± 15.3 ... 768.50 597 349.15± 6.62 090107681 16.384 CPL 11.76± 3.01 –0.71± 0.16 126.2± 14.5 ... 397.43 349 26.18± 1.97 090108020 0.768 CPL 81.89± 9.27 –0.63± 0.07 123.7± 5.75 ... 623.92 602 7.58± 0.25 090109332 14.336 CPL 5.05± 1.61 –0.71± 0.20 130.5± 18.9 ... 520.62 476 10.29± 0.95 090112332 16.384 CPL 6.05± 0.64 –1.18± 0.07 200.6± 24.6 ... 466.31 480 35.38± 2.13 090112729 17.408 CPL 29.30± 1.57 –0.81± 0.03 146.0± 4.49 ... 581.79 475 92.42± 1.67 090117632 88.066 CPL 3.02± 0.15 –1.29± 0.03 367.80± 47.2 ... 832.40 594 166.12± 9.69 090126227 11.264 CPL 15.62± 4.24 –1.09± 0.12 41.84± 2.14 ... 508.89 479 11.80± 0.42 090129880 16.384 CPL 7.34± 0.46 –1.46± 0.04 166.0± 15.1 ... 677.97 602 49.01± 2.00 090131090 30.974 Band 81.89± 9.88 –0.87± 0.05 50.66± 1.72 –2.17± 0.02 790.20 596 321.61± 9.91 090202347 18.432 Band 6.65± 0.30 –1.25± 0.03 492.6± 74.9 –2.43± 0.47 763.25 602 126.28± 32.09 090206620 0.384 CPL 25.09± 2.64 –0.58± 0.12 498.5± 75.9 ... 509.30 476 8.11± 0.88 090207777 14.336 CPL 4.99± 0.44 –1.22± 0.06 284.0± 40.7 ... 911.17 717 35.20± 2.55 090213236 17.408 CPL 2.703± 0.72 –0.38± 0.27 275.9± 52.5 ... 750.22 718 15.94 ± 2.26 090217206 34.941 CPL 11.77± 0.21 –0.88± 0.01 573.9± 18.8 ... 981.27 718 384.61± 8.04 090222179 26.624 CPL 9.49± 1.37 –0.78± 0.08 107.3± 6.29 ... 526.97 477 30.15± 1.13 090227310 16.253 CPL 4.66± 0.16 –0.94± 0.04 1301± 205 ... 730.66 604 166.12± 15.52 090227772 0.704 Band 57.06± 0.91 –0.48± 0.02 2013± 77.4 –3.15± 0.20 519.98 477 324.79± 9.85 090228204 0.512 CPL 90.36± 1.72 –0.60± 0.02 885.4± 36.7 ... 789.19 725 86.95± 2.66 090228976 9.216 CPL 5.47± 1.08 –0.93± 0.13 159.6± 20.9 ... 834.50 724 11.50± 0.82 090301315 13.312 CPL 4.28± 0.44 –1.01± 0.08 349.9± 59.4 ... 666.44 601 31.31± 3.06 090305052 3.072 CPL 6.98± 0.38 –0.66± 0.07 899.5± 129.0 ... 666.40 602 39.21± 3.99 090306245 16.384 CPL 12.67± 4.97 –0.46± 0.22 76.33± 6.14 ... 518.53 481 9.66± 0.59 090308734 1.664 CPL 20.01± 0.71 –0.56± 0.05 631.0± 39.4 ... 873.36 842 39.52± 1.70 090310189 94.209 CPL 3.48± 0.35 –1.16± 0.06 193.9± 24.0 ... 755.82 477 111.35± 6.97 090319622 67.585 CPL 4.28± 0.33 –1.05± 0.05 202.7± 15.4 ... 752.14 480 93.61± 4.17 090320801 53.25 CPL 2.67± 0.95 –1.20± 0.18 68.67± 8.67 ... 675.38 476 19.89± 1.87 090323002 197.634 CPL 8.38± 0.08 –1.38± 0.01 719.2± 34.8 ... 1861.30 584 1662.40± 35.59 090326633 13.312 CPL 10.96± 2.16 –0.97± 0.11 84.77± 5.87 ... 725.87 599 17.21± 0.75 090327404 19.456 CPL 19.06± 2.39 –0.54± 0.08 99.9± 3.64 ... 693.48 603 29.31± 0.76 090328401 67.585 CPL 9.22± 0.16 –1.07± 0.01 709.1± 29.5 ... 1312.8 718 680.2± 15.55 090328713 0.192 CPL 31.92± 1.39 –0.89± 0.05 1953± 339 ... 510.76 473 22.43± 2.95

Table 2. continued.

GRB ∆t Model aA/10−3 α Epeak β C-stat d.o.f. Fluence/10−7

s ph/cm2_{/s keV erg/cm}2 090330279 51.2 CPL 7.95± 0.39 –0.87± 0.03 224.0± 9.68 ... 674.70 587 129.90± 3.12 090409288 34.816 CPL 4.15± 1.58 –0.36± 0.28 163.3± 27.4 ... 451.95 355 20.38± 2.42 090411838 20.48 CPL 9.86± 0.57 –0.98± 0.04 228.8± 15.1 ... 499.66 482 70.58± 2.75 090411991 20.99 Band 13.22± 2.18 –0.81± 0.09 179.0± 27.9 –1.87± 0.10 714.91 355 242.7± 44.06 090413122 22.528 CPL 6.85± 1.11 –0.64± 0.11 174.1± 16.1 ... 656.14 595 30.24± 1.74 090419997 52.224 Band 8.06± 1.18 –1.16± 0.07 98.07± 11.5 –2.03± 0.06 1030.00 597 202.91± 19.83 090423330 14.336 CPL 7.19± 2.67 –1.00± 0.20 78.31± 9.98 ... 690.83 595 11.67± 1.72 090424592 34.046 Band 53.75± 0.87 –1.02± 0.01 161.9± 2.15 –3.26± 0.18 1179.00 718 501.25± 10.55 090425377 37.89 Band 10.37± 0.84 –1.37± 0.05 110.7± 9.54 –2.32± 0.13 480.57 358 164.95± 40.79 090425377 37.89 CPL 9.06± 0.47 –1.43± 0.03 134.1± 8.04 ... 483.37 359 117.6±4.75 090426690 12.288 CPL 4.73± 0.38 –1.27± 0.06 336.4± 60.3 ... 668.17 600 33.62± 2.83 090427688 15.36 Band 206.4± 157 0.70± 0.37 58.75± 4.67 -2.36± 0.11 1146 695 27.95± 3.38 090428441 6.144 CPL 27.37± 6.73 –0.55± 0.14 86.14± 5.16 ... 670.74 595 10.73± 0.47 090429753 0.832 Band 38.53± 15.60 –0.28± 0.26 178.3± 44.3 –1.65± 0.06 502.93 467 42.34± 7.08 090502777 41.985 CPL 7.11± 1.44 –1.03± 0.14 59.98± 2.79 ... 707.05 476 26.49± 1.05 090509215 20.477 CPL 4.21± 0.63 –0.80± 0.11 237.1± 33.2 ... 861.94 592 28.22± 2.46 090510016 1.536 Band 31.68± 0.64 –0.82± 0.02 4251± 312 –2.76± 0.25 490.59 479 555.84± 24.03 090510016 1.536 CPL 31.64± 0.90 –0.83± 0.02 4575± 235 ... 496.33 480 523.3±21.5 090510325 8.192 CPL 1.28± 0.17 –0.65± 0.13 2522± 594 ... 451.84 354 78.72± 15.78 090511684 5.12 CPL 5.50± 0.90 –0.94± 0.11 278.0± 58.3 ... 514.72 470 11.88± 1.49 090513916 19.456 CPL 3.66± 0.26 –0.84± 0.08 752.9± 156.0 ... 630.28 478 92.38± 13.23 090514726 6.144 CPL 8.75± 1.05 –0.96± 0.09 297.2± 47.0 ... 344.75 360 24.51± 2.30 090514734 77.825 CPL 4.30± 0.49 –1.33± 0.06 94.78± 6.4 ... 537.21 478 76.40± 2.65 090516137 132.10 CPL 4.74± 0.16 –0.99± 0.02 315.2± 15.3 ... 2576.20 717 306.99± 8.19 090516353 136.19 Band 46.04± 19.30 –0.39± 0.17 41.75± 3.04 –2.03± 0.03 599.53 238 92.62± 2.77 090516853 19.456 CPL 4.84± 0.43 –1.45± 0.05 209.6± 37.7 ... 560.41 479 44.03± 3.78 090518244 12.29 CPL 16.66± 3.30 –0.60± 0.12 107.9± 7.53 ... 370.18 355 19.54± 1.08 090519462 7.168 CPL 7.91± 2.80 –0.64± 0.23 119.5± 15.3 ... 814.68 710 6.62± 0.56 090519881 18.432 CPL 2.83± 0.36 –0.55± 0.13 439.1± 79.3 ... 824.52 709 36.74± 4.79 090520850 7.168 CPL 17.42± 2.03 –0.64± 0.08 196.4± 15.8 ... 555.18 478 28.97± 1.51 090520876 18.432 CPL 39.45± 4.28 –0.93± 0.05 45.06± 0.77 ... 585.84 595 37.92± 0.52 090522344 26.624 CPL 6.36± 2.19 –0.89± 0.20 88.33± 9.49 ... 672.96 580 18.60± 1.36 090524346 60.417 Band 31.36± 3.77 –0.72± 0.06 71.33± 2.83 –2.21± 0.04 944.97 717 263.23± 13.29 090528173 55.297 Band 37.35± 15.50 –0.75± 0.17 34.64± 2.26 –2.23± 0.03 2375.20 706 116.19± 13.27 090528516 120.83 Band 10.40± 0.32 –1.21± 0.02 181.6± 7.74 –2.31± 0.08 1874.70 721 661.55± 40.19 090529310 6.144 CPL 7.88± 1.26 –0.98± 0.10 164.9± 19.9 ... 657.42 599 11.95± 0.80 090529564 12.288 CPL 19.84± 0.87 –1.09± 0.03 244.6± 14.0 ... 646.73 592 97.99± 2.83 090530760 172.03 Band 46.21± 2.68 –0.83± 0.03 58.38± 0.94 –2.38± 0.02 2584.20 479 809.44± 14.43 090531775 1.216 CPL 7.69± 0.45 –0.69± 0.08 1729± 333 ... 621.25 475 39.35± 5.85 090602564 23.552 CPL 4.52± 0.51 –0.70± 0.11 384.4± 58.2 ... 359.26 354 62.13± 6.36 090610723 11.264 CPL 7.92± 2.80 –0.66± 0.22 110.1± 13.8 ... 730.68 472 9.49± 0.82 090612619 17.408 CPL 6.16± 0.36 –0.80± 0.05 395.4± 34.8 ... 899.22 597 65.29± 3.66 090617208 0.256 Band 39.28± 3.54 –0.37± 0.11 623.5± 99.8 –2.22± 0.24 599.87 600 24.56± 5.37 090617208 0.256 CPL 38.97± 3.72 –0.37± 0.09 652.1± 79.3 ... 601.82 601 13.75±1.36 090618353 182.27 Band 41.17± 0.56 –1.33± 0.01 162.6± 2.9 –2.52± 0.04 473.03 232 3381.40± 61.96 090618353 182.27 Band 42.48± 0.59 –1.32± 0.01 156.9± 3.59 –2.51± 0.04 641.11 234 3398.1± 62.00 090620400 17.661 Band 54.70± 2.48 –0.31± 0.03 156.7± 3.5 –2.60± 0.09 750.99 599 179.53± 9.00 090621185 65.537 Band 12.17± 2.07 –1.00± 0.08 63.36± 3.96 –2.41± 0.10 886.34 474 114.05± 9.83 090621417 38.913 CPL 4.00± 0.54 –1.20± 0.08 125.1± 12.2 ... 869.21 595 37.43± 1.87 090621922 0.128 CPL 42.44± 6.05 –0.05± 0.22 503.9± 75.4 ... 352.39 358 5.42± 0.67 090623107 60.417 CPL 6.25± 0.23 –0.72± 0.03 395.7± 21.2 ... 777.00 598 229.37± 8.46 090623913 56.321 CPL 2.44± 0.16 –1.27± 0.05 379.8± 63.8 ... 869.79 714 87.09± 7.32 090625234 25.6 CPL 3.08± 0.70 –0.82± 0.15 179.1± 29.1 ... 593.40 473 18.61± 1.82 090625560 9.216 CPL 10.26± 1.79 –0.88± 0.12 161.2± 17.7 ... 581.70 477 20.64± 1.38 090626189 64.513 Band 30.08± 0.70 –1.17± 0.01 210.7± 6.9 –2.38± 0.05 660.00 467 1057.8± 35.48 090626189 64.513 Band 31.95± 0.77 –1.15± 0.01 194.9± 6.05 –2.34± 0.05 757.78 474 1074.2± 34.82 090630311 6.144 CPL 9.74± 2.04 –1.37± 0.11 61.0± 4.68 ... 801.32 696 10.38± 0.45 090704242 86.017 CPL 4.58± 0.32 –1.17± 0.04 241.1± 25.1 ... 754.93 355 163.75± 8.00 090706283 195.59 Band 1234±2280 0.37± 0.65 17.4± 0.64 –2.68± 0.06 515.90 235 126.63± 4.39 090708152 14.336 Band 11.14± 7.70 –0.80± 0.31 51.14± 7.9 –2.58± 0.32 642.32 597 10.86± 2.15 090708152 14.336 CPL 6.58± 2.54 –1.03±0.18 59.57±5.35 ... 643.44 598 8.38±0.50 090709630 18.432 CPL 6.86± 0.93 –0.96± 0.08 137.5± 12.5 ... 700.37 600 25.12± 1.33 090711850 88.065 CPL 3.25± 0.26 –1.04± 0.06 298.3± 36.1 ... 1050.90 470 135.22± 8.46 090712160 63.489 CPL 2.09± 0.18 –0.78± 0.07 432.8± 58.3 ... 617.35 479 90.30± 7.62 090713020 49.153 Band 68.23± 11.10 0.32± 0.09 85.97± 2.27 –2.84± 0.12 3295.50 704 86.28± 4.08 090717034 68.61 Band 22.80± 1.08 –0.93± 0.03 114.9± 3.31 –2.30± 0.05 1232.10 819 431.96± 20.58

Table 2. continued.

GRB ∆t Model aA/10−3 α Epeak β C-stat d.o.f. Fluence/10−7

s ph/cm2_{/s keV erg/cm}2 090717111 0.384 CPL 9.90± 1.21 –0.19± 0.22 695.8± 132.0 ... 680.84 708 6.50± 0.96 090718762 30.717 Band 26.46± 0.81 –1.15± 0.02 164.1± 5.1 –2.81± 0.19 820.15 589 277.44± 15.05 090719063 19.71 Band 77.07± 1.53 –0.66± 0.01 228.8± 3.78 –3.14± 0.14 708.11 471 497.53± 12.02 090719063 19.71 CPL 73.70±1.24 –0.68± 0.01 239.7± 3.28 ... 716.72 472 452.7±3.75 090720276 6.144 CPL 49.05± 6.40 –0.66± 0.08 108.0± 5.01 ... 382.60 353 31.12± 0.98 090720710 17.022 CPL 6.67± 0.26 –1.00± 0.03 792.5± 92.3 ... 626.43 588 142.45± 9.88 090725838 19.456 Band 67.07± 62.40 –0.21± 0.40 45.19± 6.26 –2.21± 0.10 447.58 346 39.65± 6.35 090725838 19.456 CPL 7.80± 1.63 –1.15±0.11 81.61± 7.16 ... 454.82 347 23.27±1.19 090730608 19.46 CPL 11.74± 2.01 –0.45± 0.11 130.5± 8.49 ... 806.54 704 24.56± 1.24 090802235 0.128 CPL 113.50± 12.60 –0.61± 0.10 337.6± 37.0 ... 342.61 355 7.05± 0.54 090802666 38.913 Band 7.59± 6.40 –1.09± 0.36 38.68± 6.81 –2.42± 0.19 396.41 351 29.68± 5.05 090804940 11.264 CPL 138.40± 5.40 –0.59± 0.02 97.15± 1.07 ... 477.88 466 125.71± 0.95 090805622 59.393 Band 15.33± 11.70 –0.80± 0.34 51.46± 9.55 –2.16± 0.09 767.95 355 105.19± 19.14 090807832 6.144 Band 117.00± 148.00 –0.49± 0.49 27.36± 2.86 –2.47± 0.10 791.60 704 11.21± 0.83 090809978 19.456 Band 36.32± 1.43 –0.84± 0.02 199.5± 7.82 –2.29± 0.08 615.21 474 338.76± 25.30 090810659 112.64 Band 24.30± 18.30 –0.72± 0.30 38.96± 6.36 –1.95± 0.04 1737.50 351 336.09± 28.15 090810781 36.864 Band 60.06± 28.90 –0.21± 0.22 48.56± 3.41 –2.37± 0.08 668.28 474 58.96± 9.06 090811696 16.384 CPL 1.89± 0.22 –1.17± 0.09 778.2± 296.0 ... 1631.3 580 35.29± 6.56 090813174 9.725 CPL 8.74± 0.73 –1.50± 0.05 128.6± 12.7 ... 571.21 464 30.96± 1.26 090814368 0.576 CPL 13.50± 1.07 –0.57± 0.10 742.4± 125.0 ... 812.85 715 11.62± 1.50 090814950 173.06 CPL 1.60± 0.05 –1.26± 0.03 1679± 474 ... 684.56 348 544.44± 95.10 090815300 39.936 CPL 11.04± 4.48 0.02± 0.27 103.1± 8.28 ... 508.08 358 18.08± 1.24 090815438 24.576 Band 35.93± 11.20 –1.03± 0.13 32.36± 1.43 –2.72± 0.11 657.34 473 50.59± 2.39 090815946 60.416 CPL 3.26± 0.43 –1.04± 0.08 156.1± 17.7 ... 1466.90 586 48.93± 3.14 090819607 0.448 CPL 10.41± 1.53 –0.60± 0.19 544.5± 132.0 ... 707.48 711 4.42± 0.72 090820027 32.77 Band 167.30± 1.90 –0.67± 0.01 205.2± 1.83 –2.81± 0.04 550.05 344 1716.50± 22.27 090820509 12.288 CPL 6.69± 1.84 –1.48± 0.13 32.94± 2.93 ... 452.79 467 11.30± 0.44 090824918 56.321 CPL 19.08± 6.73 –0.90± 0.16 30.33± 1.3 ... 720.02 450 31.23± 0.96 090826068 17.408 CPL 6.80± 2.35 –0.31± 0.23 126.6± 14.1 ... 667.63 590 10.41± 0.85 090828099 86.017 Band 7.60± 0.42 –1.24± 0.03 171.2± 12.9 –2.40± 0.17 440.05 354 310.24± 37.88 090829672 93.186 Band 20.08± 0.28 –1.48± 0.01 194.7± 5.86 –2.39± 0.07 1808.90 807 1161.80± 51.27 090829702 32.768 CPL 10.96± 1.69 –0.58± 0.10 124.9± 7.5 ... 560.51 465 41.51± 1.67 090831317 48.719 CPL 5.74± 0.24 –1.52± 0.03 260.2± 28.6 ... 407.13 353 158.98± 6.83 090902401 2.048 CPL 13.28± 1.54 0.00± 0.18 419.6± 42.4 ... 543.13 472 19.17± 1.66 090902462 30.207 CPL 78.07± 0.71 –0.63± 0.01 716.3± 6.07 ... 1003.10 579 3223.60± 28.46 090904058 70.657 CPL 11.01± 0.65 –1.29± 0.03 123.2± 5.91 ... 338.52 232 208.29± 4.39 090904581 51.201 CPL 1.68± 0.23 –0.58± 0.15 434.3± 82.8 ... 1168.80 710 59.38± 9.73 090907017 39.936 CPL 5.34± 0.67 –0.36± 0.11 248.3± 21.3 ... 403.26 352 60.34± 3.87 090907808 1.024 CPL 23.82± 1.79 –0.16± 0.10 403.8± 28.5 ... 768.32 714 15.62± 0.87 090908314 65.537 CPL 2.56± 0.57 –1.27± 0.11 71.0± 6.27 ... 697.46 467 27.55± 1.58 090908341 23.677 CPL 3.03± 0.28 –0.61± 0.09 656.6± 107.0 ... 529.10 471 88.18± 10.18 090909487 26.624 CPL 9.53± 2.41 –1.20± 0.15 96.36± 11.1 ... 556.83 463 48.23± 3.47 090910812 54.273 Band 10.41± 0.66 –0.78± 0.05 246.0± 17.3 –2.35± 0.14 588.76 470 313.98± 35.81 090910812 54.273 CPL 9.48± 0.38 –0.84± 0.03 282.7±12.6 ... 594.47 471 211.5±5.97 090912660 77.825 Band 22.11± 6.03 –0.30± 0.14 69.8± 3.83 –2.71± 0.18 1383.30 463 73.93± 6.46 090912660 77.825 CPL 15.87± 2.57 –0.46± 0.09 76.53± 2.47 ... 1389.5 464 57.16± 1.40 090915650 12.288 CPL 6.04± 0.66 –0.76± 0.09 283.3± 32.9 ... 611.91 590 29.71± 2.21 090917661 30.72 CPL 2.56± 0.50 –0.82± 0.16 275.3± 56.2 ... 848.71 590 31.07± 3.69 090920035 44.032 Band 6.23± 2.14 –1.24± 0.18 89.49± 20.6 –2.16± 0.14 1219.60 470 104.15± 30.20 090922539 24.576 Band 19.53± 1.09 –0.95± 0.03 149.0± 6.7 –2.51± 0.15 1215.00 813 146.66± 11.55 090922605 36.864 CPL 4.21± 0.36 –0.97± 0.10 463.3± 70.6 ... 439.68 348 113.36± 11.38 090924625 0.192 CPL 24.80± 2.63 –0.55± 0.12 697.1± 138.0 ... 489.05 471 6.56± 1.00 090925389 29.696 Band 13.58± 2.03 –0.75± 0.09 154.2± 16.5 –2.11± 0.12 382.37 347 175.71± 27.93 090926181 19.709 Band 165.0± 1.22 –0.71± 0.005 289.9± 2.26 –2.55± 0.02 1762.3 828 1860.3± 18.55 090926181 19.709 Band 164.2± 1.21 –0.71± 0.005 291.8± 2.28 –2.55± 0.02 1514.4 816 1859.1± 18.52 090926914 65.537 CPL 33.24± 3.18 –0.19± 0.06 94.49± 1.9 ... 934.85 472 98.12± 1.59 090928646 18.432 CPL 7.49± 1.46 –0.56± 0.15 191.4± 21.8 ... 506.35 468 29.22± 1.84 090929190 13.312 CPL 10.66± 0.53 –0.62± 0.06 483.9± 36.9 ... 663.10 581 113.68± 5.46 091003191 23.552 CPL 18.54± 0.49 –0.99± 0.02 410.2± 17.2 ... 492.87 353 281.12± 6.12 091005679 16.384 CPL 4.14± 0.69 –0.89± 0.12 206.6± 30.5 ... 667.09 596 20.03± 1.80 091010113 9.216 CPL 46.96± 1.76 –1.10± 0.02 144.1± 4.05 ... 441.23 357 105.67± 1.58 091012783 0.832 CPL 36.09± 1.84 –0.46± 0.07 684.9± 59.2 ... 397.71 356 42.52± 2.62 091017985 44.033 Band 32.09± 46.30 –0.13± 0.62 43.38± 8.06 –2.23± 0.13 757.32 592 33.32± 6.60 091017985 44.033 CPL 3.51± 1.11 –1.11± 0.17 73.37± 7.75 ... 761.42 593 19.5± 1.28 091018957 0.32 CPL 28.29± 7.13 –0.53± 0.26 298.7± 61.6 ... 497.34 474 3.62± 0.48 091020900 28.672 Band 7.87± 0.81 –1.20± 0.06 186.8± 24.8 –2.29± 0.18 417.10 354 123.78± 18.06